D₈² #19967

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈²
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

D₈²

	subgroup	G/H
center, socle	C₂²	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

459 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 16 points:

(1,2,3,4,5,6,7,8);(2,8)(3,7)(4,6);(9,10,11,12,13,14,15,16);(10,16)(11,15)(12,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 12955);